- #1

utkarshakash

Gold Member

- 855

- 13

## Homework Statement

Let A be the set of all 3x3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices B in A for which the system of linear equations [itex]B \left[ \begin{array}{c} x \\ y \\ z \end{array} \right] = \left[ \begin{array}{c} 1 \\ 0 \\0 \end{array} \right] [/itex] has a unique solution is

## The Attempt at a Solution

I started by finding total number of matrices in A which comes out to be 12. Now, instead of finding matrices having unique solution I tried finding out inconsistent solutions. Now, the problem arises that how do I find these matrices. Is it by writing out all possible 12 matrices and then checking manually or applying some clever methods (which I unfortunately don't know)?